EDA for Energy Sector Fund

The Energy Sector Fund (XLE) tracks the performance of companies involved in the exploration, production, and distribution of energy. From 2010 to March 2023, the fund has shown a lot of volatility due to the fluctuating prices of oil and natural gas. During this period, the fund experienced a significant decline in 2014-2015 as oil prices dropped sharply, but it rebounded in 2016-2017 as prices stabilized. However, the fund experienced another sharp decline in 2020 due to the COVID-19 pandemic and a subsequent drop in demand for energy. The trend for this sector is closely tied to geopolitical events, global economic growth, and changes in regulations. As the world transitions towards renewable energy sources, it remains to be seen how the energy sector will perform in the future.

Time Series Plot

Code

# get data
options("getSymbols.warning4.0"=FALSE)
options("getSymbols.yahoo.warning"=FALSE)


data = getSymbols("XLE",src='yahoo', from = '2010-01-01',to = "2023-03-01")

df <- data.frame(Date=index(XLE),coredata(XLE))

# create Bollinger Bands
bbands <- BBands(XLE[,c("XLE.High","XLE.Low","XLE.Close")])

# join and subset data
df <- subset(cbind(df, data.frame(bbands[,1:3])), Date >= "2010-01-01")

#export the data 
XLE_data <- df
write.csv(XLE_data, "DATA/CLEANED DATA/XLE_raw_data.csv", row.names=FALSE)

# colors column for increasing and decreasing
for (i in 1:length(df[,1])) {
  if (df$XLE.Close[i] >= df$XLE.Open[i]) {
      df$direction[i] = 'Increasing'
  } else {
      df$direction[i] = 'Decreasing'
  }
}

i <- list(line = list(color = '#FFE4E1'))
d <- list(line = list(color = '#7F7F7F'))

# plot candlestick chart

fig <- df %>% plot_ly(x = ~Date, type="candlestick",
          open = ~XLE.Open, close = ~XLE.Close,
          high = ~XLE.High, low = ~XLE.Low, name = "XLE",
          increasing = i, decreasing = d) 
fig <- fig %>% add_lines(x = ~Date, y = ~up , name = "B Bands",
            line = list(color = '#ccc', width = 0.5),
            legendgroup = "Bollinger Bands",
            hoverinfo = "none", inherit = F) 
fig <- fig %>% add_lines(x = ~Date, y = ~dn, name = "B Bands",
            line = list(color = '#ccc', width = 0.5),
            legendgroup = "Bollinger Bands", inherit = F,
            showlegend = FALSE, hoverinfo = "none") 
fig <- fig %>% add_lines(x = ~Date, y = ~mavg, name = "Mv Avg",
            line = list(color = '#E377C2', width = 0.5),
            hoverinfo = "none", inherit = F) 
fig <- fig %>% layout(yaxis = list(title = "Price"))

# plot volume bar chart
fig2 <- df 
fig2 <- fig2 %>% plot_ly(x=~Date, y=~XLE.Volume, type='bar', name = "XLE Volume",
          color = ~direction, colors = c('#FFE4E1','#7F7F7F')) 
fig2 <- fig2 %>% layout(yaxis = list(title = "Volume"))

# create rangeselector buttons
rs <- list(visible = TRUE, x = 0.5, y = -0.055,
           xanchor = 'center', yref = 'paper',
           font = list(size = 9),
           buttons = list(
             list(count=1,
                  label='RESET',
                  step='all'),
             list(count=3,
                  label='3 YR',
                  step='year',
                  stepmode='backward'),
             list(count=1,
                  label='1 YR',
                  step='year',
                  stepmode='backward'),
             list(count=1,
                  label='1 MO',
                  step='month',
                  stepmode='backward')
           ))

# subplot with shared x axis
fig <- subplot(fig, fig2, heights = c(0.7,0.2), nrows=2,
             shareX = TRUE, titleY = TRUE)
fig <- fig %>% layout(title = paste("Energy Sector Fund Stock Price: JAN 2010 - March 2023"),
         xaxis = list(rangeselector = rs),
         legend = list(orientation = 'h', x = 0.5, y = 1,
                       xanchor = 'center', yref = 'paper',
                       font = list(size = 10),
                       bgcolor = 'transparent'))

fig

The Energy Sector Fund (XLE) is an exchange-traded fund that tracks the performance of the energy sector in the S&P 500 index. The fund includes companies involved in exploration, production, refining, and distribution of energy. From 2010 to March 2023, the XLE experienced significant fluctuations due to several factors.

In 2010-2014, the XLE saw steady growth due to rising demand for energy, increased production from shale, and higher oil prices. However, in mid-2014, the global oil market entered a period of oversupply, and oil prices crashed. This led to a sharp decline in XLE’s value, which lasted until early 2016.

Between 2016 and early 2020, XLE recovered and experienced moderate growth, fueled by global economic growth and higher demand for oil. However, in early 2020, the COVID-19 pandemic caused a sharp decline in energy demand, resulting in another crash in oil prices and a significant drop in XLE’s value.

In the second half of 2020 and early 2021, XLE began to recover as oil prices stabilized and energy demand gradually picked up. However, concerns over inflation and rising interest rates caused a drop in XLE’s value in the first quarter of 2022.

Overall, the Energy Sector Fund has been highly sensitive to fluctuations in oil prices and global energy demand, which can be affected by various factors such as geopolitical events, technological advancements, and economic conditions.

For stock prices, a multiplicative decomposition is typically preferred because the percentage changes in stock prices tend to be more important than the absolute changes. Additionally, stock prices tend to exhibit non-constant variance, meaning that the variance of the series changes over time. A multiplicative decomposition can handle this non-constant variance more effectively than an additive decomposition.

Decomposed Time Series

Decomposition Plot

Code

#time series data
myts<-ts(df$XLE.Adjusted,frequency=252,start=c(2010,01,01), end = c(2023,3,1)) 
#original plot for time series data
orginial_plot <- autoplot(myts,xlab ="Year", ylab = "Adjusted Closing Price", main = "Energy Sector Fund Stock price: JAN 2010 - March 2023")
#decompose the data
decompose = decompose(myts, "multiplicative")
#decomposition plot
autoplot(decompose)

Adjusted Decomposition Plot

Code

#adjusted plot
trendadj <- myts/decompose$trend
decompose_adjtrend_plot <- autoplot(trendadj,ylab='trend') +ggtitle('Adjusted trend component in the multiplicative time series model')
seasonaladj <- myts/decompose$seasonal
decompose_adjseasonal_plot <- autoplot(seasonaladj,ylab='seasonal') +ggtitle('Adjusted seasonal component in the multiplicative time series model')
grid.arrange(orginial_plot, decompose_adjtrend_plot,decompose_adjseasonal_plot, nrow=3)

The adjusted seasonal component tend to have upward trend till 2019 and drops during the covid period and there is more variability in the model when compared to the original plot where the variation during the years but the adjusted trend then to have more fluctuation showing no trend when compared to the original plot.

Lag Plots

Daily Time Lags

Code

#Lag plots 
gglagplot(myts, do.lines=FALSE, lags=1)+xlab("Lag 1")+ylab("Yi")+ggtitle("Lag Plot for Energy Sector Fund Stock JAN 2010 - March 2023")

Monthly Time Lags

Code

#montly data
mean_data <- df %>% 
  mutate(month = month(Date), year = year(Date)) %>% 
  group_by(year, month) %>% 
  summarize(mean_value = mean(XLE.Adjusted))
month<-ts(mean_data$mean_value,start = c(2010, 1),frequency = 12)
#Lag plot
ts_lags(month)

The first lag plot shows a scatter plot of the Energy Sector Fund stock prices against their lagged values by one time period. The plot shows a strong linear pattern, indicating a high correlation between the stock prices and their lagged values. This suggests that there is a high level of persistence in the Energy Sector Fund stock prices, meaning that the past prices are a good predictor of the future prices.

The second lag plot shows a similar pattern for the mean monthly values of the Energy Sector Fund stock prices. The plot shows a strong linear pattern, indicating a positive correlation between the mean monthly values and their lagged values by one time period. This suggests that there is a high level of persistence in the mean monthly values of the Energy Sector Fund stock prices, meaning that the past monthly means are a good predictor of the future monthly means. Overall, the lag plot outputs suggest that the Energy Sector Fund stock prices have a high level of autocorrelation, which is consistent with the trend and fluctuations in the sector.

Seasonality

Seasonal Heatmap

Code

# Create seasonal plot
ts_heatmap(month, color = "YlOrRd", title = 'Seasonality Heatmap of Energy Sector Fund Stock Jan 2010 - March 2023')

Seasonal Line plot

Code

# Create a line graph for each year with months on the x-axis
ggseasonplot(month, datecol = "date", valuecol = "value")+ggtitle("Seasonal Yearly Plot for Energy Sector Fund Stock Jan 2010 - March 2023")

The Seasonality Heatmap for the Energy Sector Fund Stock JAN 2010 - March 2023 does not reveal any clear seasonality in the data. The heatmap shows the mean value of the time series for each month and year combination, with the darker colors indicating higher values. The lack of clear patterns or darker colors in specific months or years suggests that there is no consistent seasonal pattern in the data. However, the yearly line graph shows a slight upward trend in the stock price from 2010 to 2023, but does not show any clear seasonality. Each year’s data is represented by a line, and the months are plotted on the x-axis. Overall, the lack of clear seasonality in both the heatmap and yearly line graph suggests that other factors beyond seasonality are driving the stock price fluctuations.

Moving Average

4 Month MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,5), series="4 Month MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Energy Sector Fund Stock JAN 2010 - March 2023(4 Month Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","4 Month MA"="red"),
                      breaks=c("Data","4 Month MA"))
ma

1 Year MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,13), series="1 Year MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Energy Sector Fund Stock JAN 2010 - March 2023(1 Year Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","1 Year MA"="red"),
                      breaks=c("Data","1 Year MA"))
ma

3 Year MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,37), series="3 Year MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Energy Sector Fund Stock JAN 2010 - March 2023(3 Year Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","3 Year MA"="red"),
                      breaks=c("Data","3 Year MA"))
ma

5 Year MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,61), series="5 Year MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Energy Sector Fund Stock JAN 2010 - March 2023(5 Year Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","5 Year MA"="red"),
                      breaks=c("Data","5 Year MA"))
ma

The four plots show the Energy Sector Fund stock prices from JAN 2010 to March 2023, along with the moving averages for 4 months, 1 year 3 years and 4 years. As the window of the moving average increases, the smoother the trend line becomes, reducing the impact of noise and fluctuations in the original time series.

The 4-month moving average plot shows frequent fluctuations in the stock price, with the trend line following the general direction of the time series. The 1-year moving average plot shows a smoother trend, following the overall upward trend of the stock price.

The 1-year moving average plot shows a similar trend to the 4-month plot but is even smoother, with fewer fluctuations. Finally, the 5-year moving average plot shows the smoothest trend, with downward and upward slope.As the moving average window increases, the smoother trend allows for a clearer identification of the general trend of the Energy Sector Fund stock prices over time. From the moving average obtained above we can see that there is upward tend in the stock price of Energy Sector Fund.

Autocorrelation Time Series

ACF

Code

#ACF for  data
ggAcf(month)+ggtitle("ACF Plot for Energy Sector Fund Stock JAN 2010 - March 2023")

PACF

Code

#PACF for data
ggPacf(month)+ggtitle("PACF Plot for Energy Sector Fund Stock JAN 2010 - March 2023")

ADF Test

Code

#check the stationarity
tseries::adf.test(month)

    Augmented Dickey-Fuller Test

data:  month
Dickey-Fuller = -1.5196, Lag order = 5, p-value = 0.7767
alternative hypothesis: stationary

In the plot of autocorrelation function, which is the acf graph for monthly data, there are clear autocorrelation in lag. The above lag plots and autocorrelation plot indicates seasonality in the series, which means the series is not stationary. This can be verified by the Augmented Dickey-Fuller Test which tells us that as the p value is greater than 0.05.

Detrend and Differenced Time Series

Linear Fitting Model

Code

fit = lm(myts~time(myts), na.action=NULL) 
summary(fit) 

Call:
lm(formula = myts ~ time(myts), na.action = NULL)

Residuals:
    Min      1Q  Median      3Q     Max 
-33.032  -5.253  -0.391   5.337  34.840 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.522e+03  9.807e+01  -15.52   <2e-16 ***
time(myts)   7.798e-01  4.863e-02   16.03   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 10.46 on 3277 degrees of freedom
Multiple R-squared:  0.07274,   Adjusted R-squared:  0.07245 
F-statistic: 257.1 on 1 and 3277 DF,  p-value: < 2.2e-16

ACF Plot

Code

# plot ACFs
plot1 <- ggAcf(myts, 48, main="Original Data: Energy Sector Fund Stock Stock Price")
plot2 <- ggAcf(resid(fit), 48, main="Detrended data")
plot3 <- ggAcf(diff(myts), 48, main="First differenced data")
grid.arrange(plot1, plot2, plot3, nrow=3)

The estimated slope coefficient β1, 5.359e-01 With a standard error of 4.131e-02, yielding a significant estimated increase of stock price is very less yearly. Equation of the fit for stationary process: \[\hat{y}_{t} = x_{t}+(1.029e+03)-(5.359e-01)t\]

From the above graph we can say that there is no change in detrended plot and the original data acf plot, it typically means that the data is stationary. But when the first order difference is applied the high correlation is removed but there is no seasonal correlation.

As depicted in the above figure, the series is now stationary and ready for future study.